Question

(a) Calculate the buoyant force on a 2.00-L helium balloon.

(b) Given the mass of the rubber in the balloon is 1.50 g, what is the net vertical force on the balloon if it is let go? You can neglect the volume of the rubber.

Answer 1

Answer:

0.0239364 N

0.0057879 N

Explanation:

$\rho$ = Density of the gas

g = Acceleration due to gravity = 9.81 m/s²

V = Volume

Mass of rubber = 1.5 g

Buoyant force is given by

$F_b=\rho gV\\\Rightarrow F_b=1.22\times 9.81\times 2\times 10^{-3}\\\Rightarrow F_b=0.0239364\ N$

The buoyant force is 0.0239364 N

Net vertical force is given by

$F_n=F_b-W_{He}-W_{r}\\\Rightarrow F_n=0.0239364-0.175\times 2\times 10^{-3}\times 9.81-1.5\times 10^{-3}\times 9.81\\\Rightarrow F_n=0.0057879\ N$

The net vertical force is 0.0057879 N

Answer 2

(a) The buoyant force on the helium balloon is 0.024 N.

(b) The vertical force on the balloon is 0.0147 N.

The given parameters;

• volume of the balloon, V = 2.0 L = 0.002 m³
• mass of the balloon, m = 1.5 g = 0.0015 kg
• density of air, ρ = 1.225 kg/m³

The buoyant force on the helium balloon is calculated as follows;

$F_b = \rho Vg\\\\F_b = 1.225 \times 0.002 \times 9.8\\\\F_b = 0.024 \ N$

The vertical force on the balloon is calculated as follows;

$F = mg\\\\F = 0.0015 \times 9.8\\\\F = 0.0147 \ N$

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